Annali di Matematica Pura ed Applicata

, Volume 109, Issue 1, pp 1–22 | Cite as

Non-linear operators on sets of measures

  • Richard A. Alò
  • Charles A. Cheney
  • André de Korvin


If M[, U(C, C)] is the collection of U(C, C)-valued (non-linear) set functions defined on the Borel subsets of the compact Hausdorff space S, one may define operators on M[, U(C, C)] which are « of the Hammerstein type ». We initiate a study of a concept analogous to the second dual of a space of continuous functions by inquiring as to what representation theorems one may obtain for these operators. A « Lebesgue type » decomposition theorem for elements of M[, U(C, C)] is obtained. A « density » theorem is also obtained for the space M[, U(C, C)].


Continuous Function Decomposition Theorem Hausdorff Space Compact Hausdorff Space Hammerstein Type 
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Copyright information

© Fondazione Annali di Matematica Para ed Applicata 1975

Authors and Affiliations

  • Richard A. Alò
    • 1
  • Charles A. Cheney
    • 1
  • André de Korvin
    • 2
  1. 1.PittsburghU.S.A.
  2. 2.Terre HauteU.S.A.

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